TIME-TEMPERATURE-STRESS EQUIVALENCE AND ITS APPLICATION TO NONLINEAR VISCOELASTIC MATERIALS

Stress-dependence of the intrinsic time of viscoelastic materialsis investigated. The influence of stress level on the intrinsic timeis considered to be similar to that of temperature, pressure, solventcon- centration, damage and physical aging. Thetime-temperature-stress equivalence principle is proposed, byemploying which, the creep curves at different temperatures andstress level can be shifted into a master curve at referencetemperature and stress level.

Research for time-temperature equivalence effect of rock(Ⅰ):Theory research

In order to know about the rheological properties of rock in a long range of the time scale,method of increasing temperature was brought forward to accelerate the rheological process of rock,which could extend the time scale of experimental test data.Firstly,based on the generalized linear viscoelastic constitutive equation with temperature variable,the creep behavior of rock was divided into three types according to the different strain dependences of the time,that is,Hookean deformation,Newtonian flow,and retarded elasticity.Then the general equivalence relationship between time parameter and temperature parameter was derived for each type of strain.Finally,the relation between time parameter and temperature parameter in the whole creep was considered and the general theory of time-temperature equivalence effect(TTEE) of rock was established.This research reveals: ①The temperature effect on the instantaneous strain could be modified through vertical shift.②The key point of the TTEE of Newtonian flow depends on whether in the study of linear viscoelastic behavior of rock change of temperature is completely equivalent to a shift of the logarithmic time scale or not.③By plotting the results of a creep experiment performed at different temperatures and comparing the curves obtained,one can decide whether the rock considered have TTEE.④The TTEE of the whole creep should satisfy that the horizontal shift function of Newtonian flow and retarded elasticity is consentaneous.

Research for time-temperature equivalence effect of rock(Ⅱ):Experimental research

With the creep test data of granite taken from Three Gorges,the existence of time-temperature equivalence effect(TTEE) of granite is investigated.Based on the creep test data at different temperatures,which are 20 ℃,60 ℃,80 ℃,100 ℃,200 ℃,300 ℃,four-component viscoelastic Burgers model is presented to characterize the creep curves.The parameters of elasticity modulus and viscosity coefficient in the constitutive model at different temperatures and their functional dependences on temperature are obtained.Then,according to the basic theory of TTEE presented in research(I),the TTEE of granite is investigated through modifying the compliance curves with vertical shift function and checking the coincidence of the modified curves with horizontal shift functions.It is concluded that:① Burgers model could appropriately characterize the creep property of granite in a short time scale.② Both elastic modulus and viscosity coefficient in the Burgers model decay exponentially with temperature.③ The coincidence of the curves at different temperatures after vertical shift modification and horizontal shift is fine,which indicates the existence of TTEE of granite.④The master curves which reflect the long time scale test data at temperatures 20 ℃,100 ℃,200 ℃ are obtained.

Analysis of diffusion-adsorption equivalency of landfill liner systems for organic contaminants

The equivalence between multilayered barriers regarding diffusion and adsorption was studied. The bottom boundary of the liner system is defined by assuming concentration continuous and flux continuous conditions of the contaminant between the bottom liner layer and the underlying soil. Five different liner systems were compared in terms of solute breakthrough time. The results of the analysis showed that breakthrough time of the hydrophobic organic compounds for a 2-meter-thick compacted clay liner （CCL） could be 3-4 orders of magnitude is greater than the breakthrough time for a geosynthetic clay liner （GCL） composite liner. The GM/GCL and GM/CCL composite liner systems provide a better diffusion barrier for the hydrophilic organic compounds than that for the hydrophobic compounds due to their different Henry＇s coefficient. The calculated breakthrough times of the organic contaminants for the Chinese standard liner systems were found to be generally greater than those for the GCL alternatives, for the specific conditions examined. If the distribution coefficient increases to 2.8 for the hydrophobic compounds or 1.0 for the hydrophilic compounds, the thickness of the attenuation layer needed to achieve the same breakthrough time as the standard liner systems can be reduced by a factor of about 1.9-2.4. As far as diffusive and adsorption contaminant transport are concerned, GM or GCL is less effective than CCL.

Equivalency and unbiasedness of grey prediction models

In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.

Investigation into Equivalency of Synthetic Test Circuit Used for Operational Tests of Thyristor Valves for UHVDC

With the growth of capacity of high voltage direct current(HVDC) transmission lines,the ratings of thyristor valves,which are one of the most critical equipments,are getting higher and higher.Verification of performance of thyristor valves particularly designed for HVDC project plays an important role in the handover of products between the manufacturer and the client.Conventional test facilities based on philosophy of direct test cannot meet the requirements for modern thyristor valves.New test facilities with high ratings are necessarily built based on philosophy of synthetic test.Over the conventional direct test circuit,the later is an economical and feasible solution with less financial investment and higher test capability.However,the equivalency between the synthetic test and the direct test should be analyzed technically in order to make sure that the condition of verification test in a synthetic test circuit should satisfy the actual operation condition of thyristor valves existing in a real HVDC project,just as in a direct test circuit.Equivalency analysis is focused in this paper,covering the scope of thyristor valves' steady state,and transient state.On the basis of the results achieved,a synthetic test circuit of 6 500 A/50 kV for operational tests of thyristor valves used for up to UHVDC project has newly been set up and already put into service in Xi'an High Voltage Apparatus Research Institute Co.,Ltd.(XIHARI),China.Some of the results have been adopted also by a new national standard of China.

APPLICATION OF TIME-TEMPERATURE SUPERPOSITION PRINCIPLE TO EVALUATION OF SCATTERING INTENSITY EVOLUTION IN PHASE SEPARATION FOR PMMA/SAN BLENDS

Spinodal phase separation behavior of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) blends was investigated by the time-resolved small angle light scattering (SALS) technique. It was found that the influence of temperature on the scattering intensity evolution followed the time-temperature superposition principle. The relationship between temperature and the relaxation ti me of scattering intensity I(t) can be well described by the Williams-Landel-Ferry (WLF) function.

Deterioration of equivalent thermal conductivity of granite subjected to heating-cooling treatment

Understanding the thermal conductivity of granite is critical for many geological and deep engineering applications.The heated granite was subjected to air-,water-,and liquid nitrogen(LN2-)coolings in this context.The transient hot-wire technique was used to determine the equivalent thermal conductivity(ETC)of the granite before and after treatment.The deterioration mechanism of ETC is analyzed from the meso-perspective.Finally,the numerical model is used to quantitatively study the impact of cooling rate on the microcrack propagation and heat conduction characteristics of granite.The results show that the ETC of granite is not only related to the heating temperature,but also affected by the cooling rate.The ETC of granite decreases nonlinearly with increasing heating temperature.A faster cooling rate causes a greater decrease in ETC at the same heating temperature.The higher the heating temperature,the stronger the influence of cooling rate on ETC.The main explanation for the decrease in ETC of granite is the increase in porosity and microcrack density produced by the formation and propagation of pore structure and microcracks during heating and cooling.Further analysis displays that the damage of granite at the heating stage is induced by the difference in thermal expansion and elastic properties of mineral particles.At the cooling stage,the faster cooling rate causes a higher temperature gradient,which in turn produces greater thermal stress.As a result,it not only causes new cracks in the granite,but also aggravates the damage at the heating stage,which induces a further decrease in the heat conduction performance of granite,and this scenario is more obvious at higher temperatures.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

The GMMBS Method for Time-temperature Superposition of Viscoelastic Materials

Using the time-temperature superposition principle, the dynamic properties of viscoelastic materials can be shifted to obtain a master curve. A shifting method based on the Generalized Maxwell Model （ GMMBS ） , is proposed for the time-temperature superposition process of thermo-rheological simple, linear viscoelastic materials. Experimental data points under different temperatures are all considered as a whole and expressed with one unified representation by the GMMBS, which utilizes the feature that the Generalized Maxwell Model can describe a large class of viscoelastic materials with needed accuracy. Compared with traditional overlapping window based shifting methods, the proposed constitutive model based method needn＇t judge the size or existence of the overlapping window first, and computes shift factors with useful information contained in all experimental data points. The effectiveness of the proposed method is verified by simulated data, generated from published test results, with various experimental noise levels, densities of data points and sizes of overlapping windows. It has been shown that the GMMBS is robust and accurate.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8"(203.2 mm)drill collar joint,this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions,as well as the downhole secondary makeup features,and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads.On the basis of verifying the correctness of the calculation results by using measured results in Well GT1,the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10000 m in China(Well SDTK1).The results indicate that under complex loads,the stress distribution in drill collar joints is uneven,with relatively higher von Mises stress at the shoulder and the threads close to the shoulder.For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards,when the downhole equivalent impact torque exceeds 65 kN·m,the preload balance of the joint is disrupted,leading to secondary make-up of the joint.As the downhole equivalent impact torque increases,the relative offset at the shoulder of internal and external threads increases.The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment.It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque,and effectively prevent drilling tool failure.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

Cost-Effective Monitoring of the Fuel Air Equivalence-Ratio with a Lambda Sensor and a Microcontroller in a Downdraft Biomass Gasifier

The operation of biomass treatment devices such as gasifiers is based on the control of key parameters that play an important role in product formation. These include: temperature, excess oxygen, relative humidity and biomass composition. This work focuses on excess oxygen and temperature. Unfortunately, flue gas oxygen analyzers are expensive and not accessible to small industries. However, the equivalence ratio is linked to excess oxygen and has the advantage of not depending on biomass composition. This study therefore focuses on the design and development of a device for controlling this equivalence ratio by measuring oxygen concentration using a self-propelled Lambda probe, and a system for monitoring this equivalence ratio using an Arduino Uno 3 microcontroller. The temperature is recorded with an accuracy of ±1.5°C. For a heating time of 10 minutes, the response time to temperature change is around 3 seconds, which is sufficient for the device to function properly. This simple device is an efficient and cost-effective means of checking the equivalence ratio.

From“Semantic Equivalence”to“Verve Reproduction”—Exploration on Xu Yuanchong’s English Translation of the Analects

This paper focuses on the English translation of Xu Yuanchong’s Analects,explains in depth the theory of semantic equivalence and the theory of verve reproduction.It analyzes the application and integration of these two theories by Xu Yuanchong in detail.Through a comprehensive textual analysis,this paper summarizes the remarkable achievements of the English translation of the Analects,such as the accurate transmission of semantics and the vivid reproduction of cultural charm,which is expected to bring new thinking directions and valuable references to the study of the English translation of the Analects.

Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question

Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.

The MDOF equivalent linear system and its applications in seismic analysis and design of framed structures

This paper reviews the applications of the multi degree-of-freedom(MDOF)equivalent linear system in seismic analysis and design of planar steel and reinforced concrete framed structures.An equivalent MDOF linear structure,analogous to the original MDOF nonlinear structure,is constructed,which has the same mass and elastic stiffness as the original structure and modal damping ratios that account for the effects of geometrical and material nonlinearities.The equivalence implies a balance between the viscous damping work of the equivalent linear structure and that of the nonlinearities in the original nonlinear structure.This work balance is established with the aid of a transfer function in the frequency domain.Thus,equivalent modal damping ratios can be explicitly determined in terms of the period and deformation levels of the structure as well as the soil types.Use of these equivalent modal damping ratios can help address a variety of seismic analysis and design problems associated with planar steel and reinforced concrete framed structures in a rational and accurate manner.These include force-based seismic design with the aid of acceleration response spectra characterized by high amounts of damping,improved direct displacement-based seismic design and the development of advanced seismic intensity measures.The equivalent modal damping ratios are also utilized in the context of linear modal analysis for the definition and construction of the MDOF response spectrum.Furthermore,the equivalent modal damping ratios are employed in a seismic retrofit method for steel-framed structures with viscous dampers.Finally,it is demonstrated that modal behavior(or strength reduction)factors can be easily constructed based on these modal damping ratios for a more rational and accurate force-based seismic design,including the determination of inelastic displacement profiles.

Subsidence prediction method based on equivalent mining height theory for solid backfilling mining

Based on the characteristics of strata movement of solid backfilling mining technology, the surface subsidence prediction method based on the equivalent mining height theory was proposed, and the parameters selection guideline of this method was also described. While comparing the parameters of caving mining with equivalent height, the subsidence efficient can be calculated according to the mining height and bulk factor of sagging zone and fracture zone, the tangent of main influence angle of solid backfilling mining is reduced by 0.2-0.5（while it cannot be less than 1.0）. For sake of safety, offset of the inflection point is set to zero, and other parameters, such as horizontal movement coefficient and main propagation angle are equal to the corresponding parameters of caving mining with equivalent height. In the last part, a case study of solid backfilling mining subsidence prediction was described. The results show the applicability of this method and the difference of the maximum subsidence point between the prediction and the observation is less than 5%.

Effect of gas bubble on cell voltage oscillations based on equivalent circuit simulation in aluminum electrolysis cell

A method to investigate the effect of gas bubble on cell voltage oscillations was established. The whole aluminum electrolysis cell was treated as a resistance circuit, and the dynamic simulation of the cell equivalent circuit was modeled with Matlab/Simulink simulation software. The time-series signals of cell voltage and anode current were obtained under different bubble conditions, and analyzed by spectral and statistical analysis methods. The simulation results show that higher bubble release frequency has a significant effect on the cell voltage oscillations. When the bubble coverage of one anode block exceeds 80%, the cell voltage may exceed its normal fluctuation amplitude. The simulation also proves that the anode effect detected by computer in actual production is mainly the whole cell anode effect.